The associative property refers to the way numbers are grouped in addition or multiplication. It states that when three or more numbers are added or multiplied, the way the numbers are grouped does not change the result.
Here are the basic forms of the associative property:
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Associative Property of Addition: \[ (a + b) + c = a + (b + c) \] For example: \[ (2 + 3) + 4 = 2 + (3 + 4) \] Both sides equal 9.
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Associative Property of Multiplication: \[ (a \times b) \times c = a \times (b \times c) \] For example: \[ (2 \times 3) \times 4 = 2 \times (3 \times 4) \] Both sides equal 24.
Quick Check Structures for Expressions
In your Unit 3, Lesson 4, you may encounter problems where you have to demonstrate the associative property. Here are some quick structures you might apply:
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Identify expressions using parentheses and see if regrouping them results in the same value.
Example: For the expression \( (5 + 2) + 3 \), you can regroup to \( 5 + (2 + 3) \).
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Calculate both groupings and compare results.
Example:
- \( (5 + 2) + 3 = 7 + 3 = 10 \)
- \( 5 + (2 + 3) = 5 + 5 = 10 \)
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Write your own examples using different sets of numbers or variables to illustrate the associative property.
Practice Problems
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Show that \( (1 + 4) + 6 \) is equal to \( 1 + (4 + 6) \).
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Verify \( (2 \times 5) \times 3 \) equals \( 2 \times (5 \times 3) \).
By understanding and applying the associative property, you can simplify arithmetic in various expressions effectively.
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